This article proposed a new protocol “untraceable and unclonable sensor movement in the distributed IoT environment”. The proposal has the following several advantages: (1) the new protocol using PUF achieved the main contributions of both untraceable and unclonable sensors. (2) the new protocol also achieved standard security features such as mutual authentication, perfect forward and backward secrecy. (3) The proposed authentication protocol can withstand from various kinds of attacks, such as to reply, DoS, impersonation, and cloning attack. (4) Analysis formally using BAN Logic has been conducted and denoted that the protocol achieved a secure mutual authentication. In addition, analysis formally using the RoR model and Scyther tool denoted that the proposed protocol withstands from various attacks. (5) A comparison of security features and computational complexity ensures that the proposal is secure and has low computational complexity